Finite Group Databasebeta

← #11874216

Subgroups — #11874216

Order 1152.

1185 conjugacy classes of subgroups; only the 220 normal subgroups are shown.

normal subgroups only

This group has 1185 conjugacy classes of subgroups — too many to draw. Only its 220 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63802C214yesmaximal
2#10593909C212yesmaximal
3C4×C8×C3⋊D3C211yesmaximal, characteristic
4C3×#4699C212yesmaximal, complemented
5#10590905C214yesmaximal, complemented
6#10590387C212yesmaximal, complemented
7D3×#494—32nomaximal
8C2×#3797C2214yes—
9C2×C8×C3⋊D3C2212yes—
10C42×C3⋊D3C2211yescharacteristic
11C2×C3×Dic12C2218yes—
12C3×#869C2214yes—
13#63919—24no—
14#63900—24no—
15#63873C2214yes—
16C2×#3718C2218yes—
17#63802—216no—
18C32×C4×C8C2211yescharacteristic
19C8×C3⋊Dic3C2212yes—
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C2×D3×Q16—38no—
22D3×C4⋊Q8—34no—
23C3×#494—32no—
24#5183—38no—
25#5092—34no—
26#4699D312yescomplemented
27C4×D3×C8—32no—
28C4×D3×C8—61no—
29C2×C4×C3⋊D3D412yes—
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×C3×Dic6C2318yes—
32C2×#627—24no—
33C2×#624—24no—
34#3797—216no—
35C2×C32×C8C2312yes—
36C32×C42C2311yescharacteristic
37C4×C3⋊Dic3D412yes—
38C4×C3⋊Dic3C2311yescharacteristic
39C2×C3⋊(C3⋊C8)C2312yes—
40C8×C3⋊D3D418yes—
41C3×C4⋊Dic3—28no—
42C3×Dic12—216no—
43#3724—28no—
44#3718—216no—
45C2×#494—91noSylow
46C2×D3×Q8—38no—
47C2×C3×Q16—38no—
48C3×C4⋊Q8—34no—
49#944—38no—
50C2×#216—316no—
51D3×Q16—632no—
52C2×Dic12C2×D318yes—
53C2×D3×C8—34no—
54C2×D3×C8—62no—
55D3×C4⋊C4—68no—
56#888—68no—
57C42×D3—32no—
58C42×D3—61no—
59#869C2×D314yes—
60C3×C4×C8—21no—
61C3×C4×C8C2×D312yes—
62C8×Dic3—34no—
63C8×Dic3—62no—
64C4×C3⋊C8—32no—
65C4×C3⋊C8—61no—
66C22×C3⋊D3C2×D411yescharacteristic
67C2×C32×C4C2×D412yes—
68C2×C32×C4C2411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C2×C3⋊Dic3C2×D412yes—
71C4×C3⋊D3Q1618yescomplemented
72C4×C3⋊D3C2×D414yes—
73C2×C3×Dic3—28no—
74C3×Dic6—216no—
75#627—48no—
76#624—48no—
77C32×C8C2×D414yes—
78C3⋊(C3⋊C8)C2×D414yes—
79C22×Q16—94no—
80C2×C4⋊Q8—92no—
81#494—32no—
82#494—92no—
83#494—94no—
84C2×C4×C8—91no—
85C2×C3×Q8—38no—
86D3×Q8—632no—
87C2×C4×D3—34no—
88C2×C4×D3—32no—
89C2×C4×D3—61no—
90C2×C4×D3—62no—
91C2×C4×D3—68no—
92C2×Dic6—68no—
93C2×Dic6C22×D318yes—
94C3×Q16—616no—
95C2×C3×C8—22no—
96C2×C3×C8C22×D314yes—
97C3×C4⋊C4—68no—
98C3×C42—21no—
99C3×C42C22×D312yes—
100#216—632no—
101C4⋊Dic3—28no—
102Dic3⋊C4—616no—
103C4×Dic3—34no—
104C4×Dic3—32no—
105C4×Dic3—61no—
106C4×Dic3—62no—
107C2×C3⋊C8—34no—
108C2×C3⋊C8—62no—
109Dic12—216no—
110D3×C8—316no—
111D3×C8—68no—
112C22×C32C22×D411yescharacteristic
113C2×C3⋊D3#12712yes—
114C2×C3⋊D3C2×Q1614yes—
115C32×C4C2×Q1614yescomplemented
116C32×C4C22×D412yes—
117C3⋊Dic3#12712yes—
118C3⋊Dic3C2×Q1614yescomplemented
119C3×Dic3—48no—
120C22×Q8—94no—
121C2×Q16—38no—
122C2×Q16—98no—
123C2×Q16—1816no—
124C22×C8—92no—
125C4⋊Q8—34no—
126C4⋊Q8—94no—
127C4⋊Q8—184no—
128C2×C4⋊C4—184no—
129C2×C42—91no—
130C4×C8—92no—
131C4×C8—91no—
132C4×C8D3211yescharacteristic
133C22×D3—32no—
134C22×D3—61no—
135C3×Q8—616no—
136C2×C3×C4—21no—
137C2×C3×C4—22no—
138C2×C3×C4—68no—
139C2×C3×C4D3×D414yes—
140C2×C3×C4C23×D312yes—
141C2×Dic3—28no—
142C2×Dic3—34no—
143C2×Dic3—32no—
144C2×Dic3—62no—
145C2×Dic3—61no—
146C4×D3—316no—
147C4×D3—38no—
148C4×D3—68no—
149C4×D3—64no—
150C4×D3—1216no—
151Dic6—216no—
152Dic6—1216no—
153C3×C8—24no—
154C3×C8D3×D418yes—
155C3⋊C8—38no—
156C3⋊C8—64no—
157C2×C32C2×#12711yescharacteristic
158C2×C32C22×Q1612yes—
159C3⋊D3#49414yescomplemented
160C2×Q8—38no—
161C2×Q8—184no—
162C2×Q8—1816no—
163C22×C4—91no—
164C22×C4—92no—
165C22×C4—184no—
166Q16—616no—
167Q16—1816no—
168C2×C8—92no—
169C2×C8—98no—
170C2×C8C2×D3212yes—
171C4⋊C4—68no—
172C4⋊C4—188no—
173C42—91no—
174C42—92no—
175C42C2×D3211yescharacteristic
176C22×C3—21no—
177C22×C3C2×D3×D412yes—
178C2×D3—34no—
179C2×D3—38no—
180C2×D3—62no—
181C2×D3—64no—
182C3×C4—22no—
183C3×C4—24no—
184C3×C4—128no—
185C3×C4D3×Q1618yescomplemented
186C3×C4C2×D3×D414yes—
187Dic3—34no—
188Dic3—38no—
189Dic3—48no—
190Dic3—62no—
191Dic3—64no—
192C32C2×#49411yescharacteristic, complemented, Sylow
193C23—91no—
194Q8—616no—
195Q8—368no—
196C2×C4—68no—
197C2×C4—92no—
198C2×C4—91no—
199C2×C4—94no—
200C2×C4—98no—
201C2×C4—368no—
202C2×C4#380212yes—
203C2×C4C22×D3211yescharacteristic
204C8—94no—
205C8#380214yes—
206C2×C3—22no—
207C2×C3—21no—
208C2×C3D3×#12712yes—
209C2×C3C2×D3×Q1614yes—
210D3—38no—
211D3—64no—
212C22—94no—
213C22—92no—
214C22C2×#380211yescharacteristic
215C4—94no—
216C4—92no—
217C4—128no—
218C4#6380214yescomplemented
219C4C2×#380212yes—
220C3—21no—
221C3D3×#49412yescomplemented
222C2—94no—
223C2#1059400811yescharacteristic
224C2C2×#6380212yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4×C8D32
hypocenterC32C2×#494
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C3×#4699C2semidirect
5. #10590905C2semidirect
6. #10590387C2semidirect
26. #4699D3semidirect
71. C4×C3⋊D3Q16semidirect
115. C32×C4C2×Q16semidirect
118. C3⋊Dic3C2×Q16semidirect
159. C3⋊D3#494semidirect
185. C3×C4D3×Q16semidirect
192. C32C2×#494semidirect
218. C4#63802semidirect
221. C3D3×#494semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#638022
#105939092
C4×C8×C3⋊D32
C3×#46992
#105909052
#105903872
D3×#4943